Problem: What do the following two equations represent? $-4x+4y = 3$ $-8x+8y = -5$
Putting the first equation in $y = mx + b$ form gives: $-4x+4y = 3$ $4y = 4x+3$ $y = 1x + \dfrac{3}{4}$ Putting the second equation in $y = mx + b$ form gives: $-8x+8y = -5$ $8y = 8x-5$ $y = 1x - \dfrac{5}{8}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.